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/*
* Single-precision tanh(x) function.
*
* Copyright (c) 2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "math_config.h"
#include "pl_sig.h"
#include "pl_test.h"
#define BoringBound \
0x41102cb3 /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for \
negative). */
#define AbsMask 0x7fffffff
#define One 0x3f800000
#define Shift (0x1.8p23f)
#define InvLn2 (0x1.715476p+0f)
#define Ln2hi (0x1.62e4p-1f)
#define Ln2lo (0x1.7f7d1cp-20f)
#define C(i) __expm1f_poly[i]
static inline float
expm1f_inline (float x)
{
/* Helper routine for calculating exp(x) - 1.
Copied from expm1f_1u6.c, with several simplifications:
- No special-case handling for tiny or special values, instead return early
from the main routine.
- No special handling for large values:
- No early return for infinity.
- Simpler combination of p and t in final stage of algorithm.
- |i| < 27, so can calculate t by simpler shift-and-add, instead of
ldexpf (same as vector algorithm). */
/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
float j = fmaf (InvLn2, x, Shift) - Shift;
int32_t i = j;
float f = fmaf (j, -Ln2hi, x);
f = fmaf (j, -Ln2lo, f);
/* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
Uses Estrin scheme, where the main expm1f routine uses Horner. */
float f2 = f * f;
float p_01 = fmaf (f, C (1), C (0));
float p_23 = fmaf (f, C (3), C (2));
float p = fmaf (f2, p_23, p_01);
p = fmaf (f2 * f2, C (4), p);
p = fmaf (f2, p, f);
/* t = 2^i. */
float t = asfloat ((uint32_t) (i + 127) << 23);
/* expm1(x) ~= p * t + (t - 1). */
return fmaf (p, t, t - 1);
}
/* Approximation for single-precision tanh(x), using a simplified version of
expm1f. The maximum error is 2.58 ULP:
tanhf(0x1.fa5eep-5) got 0x1.f9ba02p-5
want 0x1.f9ba08p-5. */
float
tanhf (float x)
{
uint32_t ix = asuint (x);
uint32_t iax = ix & AbsMask;
uint32_t sign = ix & ~AbsMask;
if (unlikely (iax > BoringBound))
{
if (iax > 0x7f800000)
return __math_invalidf (x);
return asfloat (One | sign);
}
if (unlikely (iax < 0x34000000))
return x;
/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
float q = expm1f_inline (2 * x);
return q / (q + 2);
}
PL_SIG (S, F, 1, tanh, -10.0, 10.0)
PL_TEST_ULP (tanhf, 2.09)
PL_TEST_INTERVAL (tanhf, 0, 0x1p-23, 1000)
PL_TEST_INTERVAL (tanhf, -0, -0x1p-23, 1000)
PL_TEST_INTERVAL (tanhf, 0x1p-23, 0x1.205966p+3, 100000)
PL_TEST_INTERVAL (tanhf, -0x1p-23, -0x1.205966p+3, 100000)
PL_TEST_INTERVAL (tanhf, 0x1.205966p+3, inf, 100)
PL_TEST_INTERVAL (tanhf, -0x1.205966p+3, -inf, 100)
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